Puzzle 36: Chromapraxia - The Zotmeister

solving the puzzle of life one entry at a time

Aug. 2nd, 2006

11:48 pm - Puzzle 36: Chromapraxia

In the same way that a phobia is a fear and a philia is a fetish (like my own kosmemophobia and kamiphilia), a praxia is a competency or skill; 'chromapraxia' is the ability to paint, something I decidedly lack. However, it's logic that will get you an image here, not artistic skill.

This puzzle design actually has quite the history, starting with controversy over who created it first. My money is on Non Ishida, who won a design contest with it, inspired by the patterns of lights created by skyscraper windows at night. It became very popular for a period, being the subject of several books, websites, video games, and a still-running regular column in GAMES Magazine. Non certainly appears to have done more for dissemination of the puzzle's popularity; it's accumulated dozens of names, but "Nishiogram" is not one of them and Nonogram is. Other names include Paint by Numbers (the GAMES Magazine title, and the title of its Wikipedia article), Griddler, Tsunami, and Logic Art; the Nikoli name is Edel.

The left is an unsolved Chromapraxia puzzle; the right is its solution. "Si, señor - it is the number two." Zorro the Gay Blade is a genius film that was ahead of its time, but I digress.

Some cells of the grid are to be colored; the objective is to determine which, and what color each is to assume. (The end result is to be interpreted as an image.) The numbers to the left of each row are the lengths of all contiguously monochromatic groups of cells within that row, the left-to-right order of those numbers matching the left-to-right order of the cell groups they refer to as they appear in that row; the numbers above each column are the lengths of all contiguously monochromatic groups of cells within that column, the top-to-bottom order of those numbers matching the top-to-bottom order of the cell groups they refer to as they appear in that column. The color of each number matches the color of the cell group it refers to.

A numbered list of rules probably won't help much, so instead, here's a casual explanation of the sample:

First of all, all the numbers outside the puzzle are black. Both the sample and the full puzzle below are only a single color. So basically, all you have to do is figure out whether any cell of the grid is to be colored black (shaded in) or left blank (I'll put a dot in those to mark them as uncolored).

See how the bottom row of the sample solution has '5' to the left of it? That means there need to be five black cells all in a row to the right of it. Of course, the whole grid is only five cells across, so the whole row is black.

Now look at the center column: it has '1 1 1' above it. This means that it needs three separate black cells - they need to be separate because you'd have a '3' above the column instead if they all ran together. In other words, there needs to be at least one space (uncolored cell) between the first and second cells, and at least one space between the second and third. (Note that if they were different color numbers, they could be right next to each other, but all the numbers here are the same color, so a space is the only thing available for separation.)

The second column from the left reads '1 2'; the '1' is above the '2'. This means that the single black cell must be higher up in the column than the two next to each other. Basically, the order of the numbers matches the order of the groups.

Once you've shaded in the cells needed to make all the numbers outside the grid accurate, you've not only solved the puzzle, but made a picture! For the sample, it's just the digit '2' in my pixelled style - not exactly Picasso, but hey, it's a start.

If you understand the instructions, the sample puzzle is really easy. If you don't, I'll accept the blame and try to make it up to you here:

(Start of sample puzzle solution)I start with the bottom row, as it's obvious. That '5' means I need to fill in five cells in that row. There only are five cells in that row, so they all get shaded in. Now, each of those five cells is also in a column, and is being referred to by a number in a column. Actually, since all these cells are on the grid's bottom, they have to belong to the numbers at the bottom. Take the leftmost column: the bottom number is '1', so the bottom of that column must contain a single black cell - it can't have another black cell right above it, or otherwise there'd be a '2' there instead. I put a dot in the cell above the bottom-left corner as a reminder that it can't possibly be filled in. The second column from the left has a '2' at the bottom, so I blacken the cell just above the bottom of that column, and then dot the cell above that one. The other three columns are just like the first. I now have eleven cells marked. The second row from the bottom is completely marked; as a precaution, I check it against its numbers: it has a single black cell, and a single '1' next to it. Those match, so I'm okay.

I turn my attention to the center column. It also has only a single possibility; I could have started there if I wanted to, but the '5' was easier to see. The '1 1 1' above it calls for three black cells, none of which are touching each other (there'd be a '2' or '3' up there instead if any were side-by-side). Alternatively, this could be thought of as needing one black cell, then at least one space, then another black cell, then at least one more space, and finally one more black cell. This is a minimum of five cells, and that's exactly how many are in the column total, so the column strictly alternates between black and uncolored, black first. The column to the right of this one is solved identically. The center row now has its group of two, so I dot the two remaining unmarked cells in that row.

What next? Hmm. No row or column is completely obvious at this stage. However, part of one is. The top row is to hold a group of black cells three long, and no others. Already, there are two black cells in that row. The third must be next to those, at one end or the other. Therefore, the cell in the upper-left corner can't be black. Dotting it, I see the leftmost column is now defined. The second row falls shortly thereafter, upon dotting the cell to the right of the one I just shaded in; the rightmost column then tells me how to finish the top row.(End of sample puzzle solution)

In keeping with the Puzzle Japan theme, this puzzle is monochromatic - all black cells, no other colors, just like the Edel formerly of that website. In Nikoli style, I'll also provide a small hint for the image: "Puzzle champion". I'll still be pretty impressed if you can tell me what it's supposed to be, though. - ZM